5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e0fc09f9-06ea-4528-a2de-f409112d85cc-06_830_1397_205_333}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a capacitated, directed network. The network represents a system of pipes through which fluid can flow.
The weights on the arcs show the lower capacities and upper capacities for the corresponding pipes, in litres per second.
- State the source node.
- Explain why the sink node must be G.
- Calculate the capacity of the cut \(C _ { 1 }\)
- Assuming that a feasible flow exists,
- explain why arc JH must be at its upper capacity,
- explain why arcs AD and CD must be at their lower capacities.
- Use Diagram 1 in the answer book to show a flow of 18 litres per second through the system.
- Prove that the answer to (e) is the maximum flow through the system.